diff --git a/x-pack/platform/plugins/shared/task_manager/server/task_claimers/strategy_mget.test.ts b/x-pack/platform/plugins/shared/task_manager/server/task_claimers/strategy_mget.test.ts
index 8f732c29bb433..8dd3011fe6449 100644
--- a/x-pack/platform/plugins/shared/task_manager/server/task_claimers/strategy_mget.test.ts
+++ b/x-pack/platform/plugins/shared/task_manager/server/task_claimers/strategy_mget.test.ts
@@ -49,6 +49,7 @@ jest.mock('../constants', () => ({
     'yawn',
     'sampleTaskSharedConcurrencyType1',
     'sampleTaskSharedConcurrencyType2',
+    'sampleTaskZeroMaxConcurrency',
   ],
 }));
 
@@ -2347,6 +2348,50 @@ describe('TaskClaiming', () => {
         { tags: ['taskClaiming', 'claimAvailableTasksMget'] }
       );
     });
+
+    test('should not claim the tasks that has 0 maxConcurrency (pollEnabled:false)', async () => {
+      const definitions = new TaskTypeDictionary(mockLogger());
+      definitions.registerTaskDefinitions({
+        foo: {
+          title: 'foo',
+          createTaskRunner: jest.fn(),
+        },
+        bar: {
+          title: 'bar',
+          createTaskRunner: jest.fn(),
+        },
+        baz: {
+          title: 'baz',
+          createTaskRunner: jest.fn(),
+        },
+        sampleTaskZeroMaxConcurrency: {
+          title: 'report',
+          createTaskRunner: jest.fn(),
+          maxConcurrency: 0,
+        },
+      });
+      const { taskClaiming, store } = initialiseTestClaiming({
+        storeOpts: {
+          definitions,
+        },
+        taskClaimingOpts: {
+          maxAttempts: 5,
+        },
+      });
+
+      await taskClaiming.claimAvailableTasksIfCapacityIsAvailable({
+        claimOwnershipUntil: new Date(),
+      });
+
+      const searchQuery = store.msearch.mock.calls[0]?.[0]?.[0].query;
+      const searchQueryMust = searchQuery?.bool?.must;
+
+      expect(Array.isArray(searchQueryMust) && searchQueryMust[1]).toEqual({
+        bool: { must: [{ terms: { 'task.taskType': ['foo', 'bar', 'baz'] } }] },
+      });
+
+      expect(JSON.stringify(searchQuery)).not.toContain('sampleTaskZeroMaxConcurrency');
+    });
   });
 
   describe('task events', () => {
diff --git a/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.test.ts b/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.test.ts
index 31fd90b8c6ec6..13b511c735a59 100644
--- a/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.test.ts
+++ b/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.test.ts
@@ -130,6 +130,26 @@ describe('CostCapacity', () => {
     ).toBe(4);
   });
 
+  test('availableCapacity returns 0 for the task type when task type with maxConcurrency is 0', () => {
+    const pool = new CostCapacity({ capacity$: of(10), logger });
+
+    const tasksInPool = new Map([
+      ['1', { ...mockTask({}, { type: 'type1' }) }],
+      ['2', { ...mockTask({}, { cost: TaskCost.Tiny }) }],
+      ['3', { ...mockTask() }],
+    ]);
+
+    expect(
+      pool.availableCapacity(tasksInPool, {
+        type: 'type1',
+        maxConcurrency: 0,
+        cost: TaskCost.Normal,
+        createTaskRunner: jest.fn(),
+        timeout: '5m',
+      })
+    ).toBe(0);
+  });
+
   describe('determineTasksToRunBasedOnCapacity', () => {
     test('runs all tasks if there is capacity', () => {
       const pool = new CostCapacity({ capacity$: of(10), logger });
diff --git a/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.ts b/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.ts
index f5e5a0ec42a5b..3b87d7bfab77a 100644
--- a/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.ts
+++ b/x-pack/platform/plugins/shared/task_manager/server/task_pool/cost_capacity.ts
@@ -6,6 +6,7 @@
  */
 
 import type { Logger } from '@kbn/core/server';
+import { isNullish } from 'utility-types';
 import { DEFAULT_CAPACITY } from '../config';
 import type { TaskDefinition } from '../task';
 import type { TaskRunner } from '../task_running';
@@ -69,7 +70,7 @@ export class CostCapacity implements ICapacity {
     taskDefinition?: TaskDefinition | null
   ): number {
     const allAvailableCapacity = this.capacity - this.usedCapacity(tasksInPool);
-    if (taskDefinition && taskDefinition.maxConcurrency) {
+    if (taskDefinition && !isNullish(taskDefinition.maxConcurrency)) {
       // calculate the max capacity that can be used for this task type based on cost
       const maxCapacityForType = taskDefinition.maxConcurrency * taskDefinition.cost;
       return Math.max(
diff --git a/x-pack/platform/plugins/shared/task_manager/server/task_pool/worker_capacity.ts b/x-pack/platform/plugins/shared/task_manager/server/task_pool/worker_capacity.ts
index 21704c7c4259f..dd9b56b5a4b8d 100644
--- a/x-pack/platform/plugins/shared/task_manager/server/task_pool/worker_capacity.ts
+++ b/x-pack/platform/plugins/shared/task_manager/server/task_pool/worker_capacity.ts
@@ -6,6 +6,7 @@
  */
 
 import type { Logger } from '@kbn/core/server';
+import { isNullish } from 'utility-types';
 import type { TaskRunner } from '../task_running';
 import type { CapacityOpts, ICapacity } from './types';
 import type { TaskDefinition } from '../task';
@@ -60,7 +61,7 @@ export class WorkerCapacity implements ICapacity {
     taskDefinition?: TaskDefinition | null
   ): number {
     const allAvailableCapacity = this.capacity - this.usedCapacity(tasksInPool);
-    if (taskDefinition && taskDefinition.maxConcurrency) {
+    if (taskDefinition && !isNullish(taskDefinition.maxConcurrency)) {
       // calculate the max workers that can be used for this task type
       return Math.max(
         Math.min(